Here we model the indeterministic dynamics of a scalar field \(\chi (x)\) . The material laid out here is based on work done in [1]}[2]}, in conjunction with A. Caticha. Our current presentation extends the efforts of IAC and the previous chapter in one crucial way: we allow the background geometry to become dynamical. Following DHKT in their development of a manifestly covariant classical geometrodynamics, the transition to a dynamical background is not accomplished by any modification to the “embeddability" conditions of DHKT, but by an appropriate choice of variables for describing the evolving geometry. The result is a hybrid ED model that approaches quantum field theory in a fixed background in one limit and approaches classical general relativity in another limit, but is not fully described by either. In particular, the model shares some formal similarities with the so-called Semi-classical Einstein equations (SCEE) (see e.g., [3]}), but here we model the fluctuations of the quantum fields and derive their coupling to gravity from first principles without the ad hoc arguments typically used to justify the SCEE.
